Damped Harmonic Motion

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The position and kinetic energy of a cart in damped harmonic motion are related. When the cart is at an extreme position, the speed is zero, and so is the energy. The energy goes through two cycles for every one cycle of position.

Lots of things vibrate, or oscillate, in harmonic motion. Most of them eventually stop, and so are described by the term “damped harmonic motion.” Richard Born, from Northern Illinois University, has put together a nice investigation of this motion using a Vernier Encoder System, two Dual Range Force Sensors, a Photogate, and springs from the Springs Set.

He attached the springs to either end of a dynamics cart and then measured the spring tension using force sensors. The motion encoder records the cart position, and the photogate is used to acquire a precise period for the motion.

Once the motion is recorded, the mathematical modeling of the motion, force, and energy can be done.